# A picture 11 inches by 15 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the boarder be if the area of the mounted picture is 285 square inches?

Oct 2, 2017

$15$ inches by $19$ inches.

#### Explanation:

If picture measures 11 inches by 15 inches its area would be:

$11 \times 15$

since we require a border with an even amount all round, we can say that the measurements will now be:

$11 + x$ and $15 + x$:

Area would be:

$\left(11 + x\right) \times \left(15 + x\right)$

This has to equal 285 square inches, so:

$\left(11 + x\right) \left(15 + x\right) = 285$

Multipying brackets:

${x}^{2} + 26 x + 165 = 285 \implies {x}^{2} + 26 x - 120 = 0$

Solve for $x$ by factorising:

$\left(x + 30\right) \left(x - 4\right) = 0 \implies x = - 30 , x = 4$

We can ignore the result $x = - 30$ since we are adding to original dimensions, not subtracting.

So we now have dimensions of:

$11 + 4 = 15$ and $15 + 4 = 19$

Area is:

$15 \times 19 = 285$

So dimensions are:

$15$ inches by $19$ inches.